Though the Longhorn State’s thumb is certainly on the scale, Mr. Cruz gets 25 percent of the vote — besting Sen. Rand Paul of Kentucky’s 13 percent and Sen. Marco Rubio of Florida’s 11 percent — and the poll demonstrates the extent to which the freshman has made a splash in D.C. in the short time since his 2012 election. He’s joined with staunch conservatives like Mr. Paul, Mr. Rubio and Sen. Mike Lee of Utah to oppose even his own party in many cases, drawing the ire of old Republican bulls like Sen. John McCain of Arizona but delighting the party base.

“What you’re seeing here with the Cruz number is that he has become the pre-eminent rising conservative in Texas,” poll co-director Jim Henson, who runs the Texas Politics Project at the University of Texas at Austin, told the Tribune. “What we’re witnessing in the numbers is Cruz running ahead and reaching back for the baton, and Rick Perry has the baton. The only question is whether Rick Perry is ready to hand it to him.”

Indeed, Mr. Perry, the state’s governor whose 2012 presidential bid ultimately flamed out after an ill-timed memory lapse during one of the primary debates, actually came in fourth with 10 percent of the vote. New Jersey Gov. Chris Christie tied for fifth at 8 percent with 2012 Vice Presidential nominee Paul Ryan.

Meanwhile, on the Democratic side, about two-thirds of Democratic voters in the poll prefer former Secretary of State Hillary Rodham Clinton for 2016, compared to 11 percent for Vice President Joseph R. Biden and 3 percent who say someone else.

The weighted margin of error for the overall poll of 1,200 registered voters is 3.3 percentage points. Among 492 voters who say they usually vote in Republican primaries, the weighted margin of error is 5.27 percentage points and among 376 voters who say they usually vote in Democratic primaries, the weighted margin of error is 5.89 percentage points.